Structural, Vibrational, and Thermal Properties of Densified Silicates
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Structural, vibrational and thermal properties of densified silicates : insights from Molecular Dynamics M. Bauchy Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, Boîte 121, 4, Place Jussieu, 75252 Paris Cedex 05, France (Dated: August 17, 2018) Structural, vibrational and thermal properties of densified sodium silicate (NS2) are investigated with classical molecular dynamics simulations of the glass and the liquid state. A systematic investi- gation of the glass structure with respect to density was performed. We observe a repolymerization of the network manifested by a transition from a tetrahedral to an octahedral silicon environment, the decrease of the amount of non-bridging oxygen atoms and the appearance of three-fold coor- dinated oxygen atoms (triclusters). Anomalous changes in the medium range order are observed, the first sharp diffraction peak showing a minimum of its full-width at half maximum according to density. The previously reported vibrational trends in densified glasses are observed, such as the shift of the Boson peak intensity to higher frequencies and the decrease of its intensity. Finally, we show that the thermal behavior of the liquid can be reproduced by the Birch-Murnaghan equation of states, thus allowing us to compute the isothermal compressibility. I. INTRODUCTION inhomogeneities and preferential diffusion pathways for sodium atoms10–16. Simulations from Cormack and co- 17–19 In the field of oxides, silicate glasses and melts have re- workers have shown a very good agreement with ex- 11,20,21 ceived a huge attention for their important applications perimental results on structure. Vibrational and 22 in materials science and geophysics, such as magma dy- elastic properties of the glass at ambient pressure have namics and properties. Pressure (or density) is obviously also been studied and successfully compared to experi- one of the most important thermodynamic variable for mental data. Using superomputers, large scale classical 23 geochemical processes in the mantle and crust. Indeed, simulations have recently been performed , as well as ab 24–26 interesting macroscopic properties of silicate melts, such initio Molecular Dynamics simulations . However, to as viscosity or diffusion, show significant changes with our knowledge, no systematic study of the evolution of pressure.1,2 the system according to pressure has been performed so Many experimental studies on silicate glasses, the far. base material for various multi-components silicate sys- We present here Molecular Dynamics simulation allow- tems, have suggested that those macroscopic proper- ing a systematic description of the structural, vibrational ties were related to atomic-scale structural changes3 and thermodynamics properties of densified glassy and such as angles4,5 or coordination number5–7. Densified liquid sodium silicate. We focus in one particular com- sodium silicate is a very interesting system to be in- position (NS2) and study the properties with increasing vestigated as it shows the effect of polymerization and density. Results show that a transition from tetrahedral depolymerization5,7. Indeed, in the silica network, Si to octahedral silicon environment occurs and that the tetrahedrons are connected by bridging oxygen atoms medium range order shows anomalous changes. Vibra- (BOs). Sodium silicate is usually described as a base sil- tional properties are also found to be very sensitive to ica network which is depolymerized by the sodium atoms. pressure and we report some trends about the behavior In this view, sodium cations break Si-BO-Si bonds and of the Boson peak according to density. Eventually, an induce non-bringding oxygen atoms (NBOs). On the con- equation of state model is proposed, thus allowing the trary, pressure tends to repolymerize the network by a computation of the isothermal compressibility. global increase of coordination numbers. The article is organized as follows. In section II, we present the numerical model and methodology that has arXiv:1203.6033v2 [cond-mat.mtrl-sci] 3 Apr 2012 Sodium silicate glass has already been extensively studied at ambient pressure using Molecular Dynamics been used. In section III, we report structural, topo- (MD). The first reported MD simulation of sodium sili- logical and vibrational results of the glass. In section cate glass in 1979 was based on a very small system (200 IV, thermodynamics and structural results of the liquid atoms) but it is remarkable to see that it presented a state are presented. Finally, section V summarizes these very reasonable structural description of the glass. Since results. this work, the used potentials have been continuously improved to get a better reproduction of experimental results. Progress in computing facilities progressively al- II. SIMULATION DETAILS lowed to reach longer time scales, thus making it possible to study diffusion at lower temperature and rheological As just mentioned, (Na2O)x - (SiO2)1−x with x=0.30 properties8,9. The possibility to simulate larger systems system has been chosen (close to the so-called NS2 system has also permitted to put in evidence the existence of with x=0.33). The simulated system is composed of N = 2 3000 atoms (700 Si, 1700 O and 600 Na), placed in a cubic box of various lengths L to study different densities (from 1.5 g/cm3 to 5.4 g/cm3). To do so, all the simulations were run in the canonical ensemble (NVT). The room 5 temperature density27 of 2.466 g/cm3 is obtained with L=34.43A.˚ A computed pressure P = -1.6 GPa is found in the glass at this density. To take into account the oxidation state of atoms18, 4 partial charges are used for the Coulomb interaction, while the short-range Buckingham potential is of the -3 form : ρ = 4.5 g cm 3 r Cij (r) Vij (r)= Aij exp(− ) − 6 (1) T ̺ij r g -3 ρ = 3.5 g cm where Aij , ̺ij and Cij are parameters which have been 2 fitted by Teter18. Usually, the Buckingham potential can induce spurious effects at high temperature (as V(r) can -3 go to negative infinity when r is close to zero, which ρ = 2.5 g cm leads to a collapse of the interacting atoms28. As de- 1 17 nij scribed in , a repulsive term Bij /r was introduced at short distance in order for the potential energy and its derivative to be continuous at r0 to avoid this issue. This potential has been extensively used by Cormack 0 et al.17,18 and has revealed a very good description of the 2 4 6 8 glass at room density for various compositions. The ef- r (Å) fect of pressure on such systems using classical Molecular Dynamics has been considered29 only at high tempera- ture for the NS4 silicate by using a Born-Mayer interac- tion potential fairly similar to the one that is presently FIG. 1: (Color online) Total radial correlation function of MD used. While, at ambient pressure, the use of a Coulomb modeled sodium silicate glasses for increasing densities and comparison with neutron diffraction studies (white rounds) interaction with fixed partial charges is supported by the 36 ionic character of the interactions and the absence of from the work of Wright et al. (Neutron diffraction data). charge transfer, one may wonder to what extent fixed charges can be still considered with increasing pressure. 6 While we are not aware of any report of densified sili- 6000 K during 10 steps (2ns). Each melt was then con- cates, a recent ab initio Molecular Dynamics study (in tinuously cooled down to the selected temperature (from which electrons and charge transfer are explicitly com- 300 K to 4000 K) using a cooling rate of 10 K/ps. puted) on an oxide network-forming glass under high pressure30,31 has not shown any deformations of the elec- III. GLASS tronic cloud that would be significant enough for ambient pressure pseudopotentials to be modified. The mentioned example30,31, the consistency of the presently reported A. Real space properties results and the fact that the present potential was suc- cessfully used to reproduce a diffusion anomaly of O and 1. Total radial correlation functions Si atoms with increasing density16,32, also observed in 33 34 pure silica or water , suggest that a certain degree of The total correlation functions gT(r) for increasing confidence can be expected. densities are shown in Fig. 1. To check the validity of Classical Molecular Dynamics simulations were per- the simulated glass, comparison with experimental data formed using the DLPOLY package35. The equations (neutron diffraction from the work of Wright et al.36) of motion were integrated with the Verlet-Leapfrog algo- at room pressure was made. We recover the same level rithm, using a timestep of 2.0 fs. Coulomb interactions of agreement than in previous studies17,19. However, we were evaluated by the Ewald summation method with a notice an increased structured system with main peaks cutoff of 12.0 A.˚ The short-range interaction cutoff was being sharper as compared to experiments. This com- chosen at 8.0 A.˚ As mentioned, the simulations were parison has also been done by Cormack17. Using the run in the canonical ensemble (NVT) with a Berendsen same potential, a better agreement has been observed thermostat. by broadening the total correlation functions.37 The po- For each density, the system was first equilibrated at sition of the first Si-O peak is well reproduced, but is 3 found to be sharper than in experiments. The position 3. Coordination numbers of the second O-O peak is also well reproduced, suggest- ing a realistic O-Si-O angle in simulation. On the other In pure silica, the network in fully connected and the ˚ hand, simulation produces a peak at 3.1A arising from coordination number CN of Si and O atoms are found Si-Si correlations (see below) which is not present in ex- to be 4 and 2, in agreement with the stoichiometry of periments but merged with other contributions in the the glass (CN N = CN N ).